1 Data preparation

1.1 Outline

  • Load scripts: loads libraries and useful scripts used in the analyses; all .R files contained in scripts at the root of the factory are automatically loaded

  • Load data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.

1.2 Load packages


library(reportfactory)
library(here)
library(rio) 
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)

1.3 Load scripts

These scripts will load:

  • all scripts stored as .R files inside /scripts/
  • all scripts stored as .R files inside /src/

These scripts also contain routines to access the latest clean encrypted data (see next section).


reportfactory::rfh_load_scripts()

1.4 Load clean data

We import the latest NHS pathways data:


x <- import_pathways() %>%
  as_tibble()
x
## # A tibble: 248,118 x 11
##    site_type date       sex   age   ccg_code ccg_name count postcode nhs_region
##    <chr>     <date>     <chr> <chr> <chr>    <chr>    <int> <chr>    <chr>     
##  1 111       2020-03-18 fema… miss… e380000… nhs_glo…     1 gl34fe   South West
##  2 111       2020-03-18 fema… miss… e380001… nhs_sou…     1 ne325nn  North Eas…
##  3 111       2020-03-18 fema… 0-18  e380000… nhs_air…     8 bd57jr   North Eas…
##  4 111       2020-03-18 fema… 0-18  e380000… nhs_ash…     7 tn254ab  South East
##  5 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    35 rm13ae   London    
##  6 111       2020-03-18 fema… 0-18  e380000… nhs_bar…     9 n111np   London    
##  7 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    11 s752py   North Eas…
##  8 111       2020-03-18 fema… 0-18  e380000… nhs_bas…    19 ss143hg  East of E…
##  9 111       2020-03-18 fema… 0-18  e380000… nhs_bas…     6 dn227xf  North Eas…
## 10 111       2020-03-18 fema… 0-18  e380000… nhs_bat…     9 ba25rp   South West
## # … with 248,108 more rows, and 2 more variables: day <int>, weekday <fct>

We also import demographics data for NHS regions in England, used later in our analysis:


path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
##                  nhs_region variable      value
## 1                North West     0-18 0.22538599
## 2  North East and Yorkshire     0-18 0.21876449
## 3                  Midlands     0-18 0.22564656
## 4           East of England     0-18 0.22810783
## 5                    London     0-18 0.23764782
## 6                South East     0-18 0.22458811
## 7                South West     0-18 0.20799797
## 8                North West    19-69 0.64274078
## 9  North East and Yorkshire    19-69 0.64437753
## 10                 Midlands    19-69 0.63876675
## 11          East of England    19-69 0.63034229
## 12                   London    19-69 0.67820084
## 13               South East    19-69 0.63267336
## 14               South West    19-69 0.63176131
## 15               North West   70-120 0.13187323
## 16 North East and Yorkshire   70-120 0.13685797
## 17                 Midlands   70-120 0.13558669
## 18          East of England   70-120 0.14154988
## 19                   London   70-120 0.08415135
## 20               South East   70-120 0.14273853
## 21               South West   70-120 0.16024072

Finally, we import publically available deaths per NHS region:


dth <- import_deaths() %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

#truncation to account for reporting delay
delay_max <- 21

dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
##      date_report               nhs_region deaths
## 1     2020-03-01          East of England      0
## 2     2020-03-02          East of England      1
## 3     2020-03-03          East of England      0
## 4     2020-03-04          East of England      0
## 5     2020-03-05          East of England      0
## 6     2020-03-06          East of England      1
## 7     2020-03-07          East of England      0
## 8     2020-03-08          East of England      0
## 9     2020-03-09          East of England      1
## 10    2020-03-10          East of England      0
## 11    2020-03-11          East of England      0
## 12    2020-03-12          East of England      0
## 13    2020-03-13          East of England      1
## 14    2020-03-14          East of England      2
## 15    2020-03-15          East of England      2
## 16    2020-03-16          East of England      1
## 17    2020-03-17          East of England      1
## 18    2020-03-18          East of England      5
## 19    2020-03-19          East of England      4
## 20    2020-03-20          East of England      2
## 21    2020-03-21          East of England     11
## 22    2020-03-22          East of England     12
## 23    2020-03-23          East of England     11
## 24    2020-03-24          East of England     19
## 25    2020-03-25          East of England     26
## 26    2020-03-26          East of England     36
## 27    2020-03-27          East of England     38
## 28    2020-03-28          East of England     28
## 29    2020-03-29          East of England     43
## 30    2020-03-30          East of England     45
## 31    2020-03-31          East of England     70
## 32    2020-04-01          East of England     62
## 33    2020-04-02          East of England     65
## 34    2020-04-03          East of England     80
## 35    2020-04-04          East of England     71
## 36    2020-04-05          East of England     76
## 37    2020-04-06          East of England     71
## 38    2020-04-07          East of England     93
## 39    2020-04-08          East of England    111
## 40    2020-04-09          East of England     87
## 41    2020-04-10          East of England     74
## 42    2020-04-11          East of England     92
## 43    2020-04-12          East of England    100
## 44    2020-04-13          East of England     78
## 45    2020-04-14          East of England     61
## 46    2020-04-15          East of England     82
## 47    2020-04-16          East of England     74
## 48    2020-04-17          East of England     86
## 49    2020-04-18          East of England     64
## 50    2020-04-19          East of England     67
## 51    2020-04-20          East of England     67
## 52    2020-04-21          East of England     75
## 53    2020-04-22          East of England     67
## 54    2020-04-23          East of England     49
## 55    2020-04-24          East of England     66
## 56    2020-04-25          East of England     54
## 57    2020-04-26          East of England     48
## 58    2020-04-27          East of England     46
## 59    2020-04-28          East of England     58
## 60    2020-04-29          East of England     32
## 61    2020-04-30          East of England     45
## 62    2020-05-01          East of England     49
## 63    2020-05-02          East of England     29
## 64    2020-05-03          East of England     41
## 65    2020-05-04          East of England     19
## 66    2020-05-05          East of England     36
## 67    2020-05-06          East of England     31
## 68    2020-05-07          East of England     33
## 69    2020-05-08          East of England     33
## 70    2020-05-09          East of England     29
## 71    2020-05-10          East of England     22
## 72    2020-05-11          East of England     18
## 73    2020-05-12          East of England     21
## 74    2020-05-13          East of England     27
## 75    2020-05-14          East of England     26
## 76    2020-05-15          East of England     19
## 77    2020-05-16          East of England     26
## 78    2020-05-17          East of England     17
## 79    2020-05-18          East of England     25
## 80    2020-05-19          East of England     15
## 81    2020-05-20          East of England     26
## 82    2020-05-21          East of England     21
## 83    2020-05-22          East of England     13
## 84    2020-05-23          East of England     12
## 85    2020-05-24          East of England     17
## 86    2020-05-25          East of England     25
## 87    2020-05-26          East of England     14
## 88    2020-05-27          East of England     12
## 89    2020-05-28          East of England     17
## 90    2020-05-29          East of England     16
## 91    2020-05-30          East of England      9
## 92    2020-05-31          East of England      8
## 93    2020-06-01          East of England     17
## 94    2020-06-02          East of England     14
## 95    2020-06-03          East of England     10
## 96    2020-06-04          East of England      7
## 97    2020-06-05          East of England     14
## 98    2020-06-06          East of England      5
## 99    2020-06-07          East of England      9
## 100   2020-06-08          East of England      7
## 101   2020-06-09          East of England      6
## 102   2020-06-10          East of England      8
## 103   2020-06-11          East of England      1
## 104   2020-06-12          East of England      9
## 105   2020-06-13          East of England      5
## 106   2020-06-14          East of England      4
## 107   2020-06-15          East of England      8
## 108   2020-06-16          East of England      3
## 109   2020-06-17          East of England      7
## 110   2020-06-18          East of England      4
## 111   2020-06-19          East of England      7
## 112   2020-06-20          East of England      4
## 113   2020-06-21          East of England      3
## 114   2020-06-22          East of England      6
## 115   2020-06-23          East of England      5
## 116   2020-06-24          East of England      4
## 117   2020-06-25          East of England      1
## 118   2020-06-26          East of England      5
## 119   2020-06-27          East of England      6
## 120   2020-06-28          East of England      8
## 121   2020-06-29          East of England      4
## 122   2020-06-30          East of England      5
## 123   2020-07-01          East of England      2
## 124   2020-07-02          East of England      5
## 125   2020-07-03          East of England      0
## 126   2020-07-04          East of England      3
## 127   2020-07-05          East of England      1
## 128   2020-07-06          East of England      2
## 129   2020-07-07          East of England      2
## 130   2020-07-08          East of England      0
## 131   2020-07-09          East of England      8
## 132   2020-07-10          East of England      4
## 133   2020-07-11          East of England      2
## 134   2020-07-12          East of England      1
## 135   2020-07-13          East of England      8
## 136   2020-07-14          East of England      2
## 137   2020-07-15          East of England      0
## 138   2020-07-16          East of England      0
## 139   2020-07-17          East of England      0
## 140   2020-07-18          East of England      0
## 141   2020-07-19          East of England      1
## 142   2020-07-20          East of England      1
## 143   2020-07-21          East of England      1
## 144   2020-07-22          East of England      2
## 145   2020-07-23          East of England      1
## 146   2020-07-24          East of England      1
## 147   2020-07-25          East of England      0
## 148   2020-07-26          East of England      1
## 149   2020-07-27          East of England      1
## 150   2020-07-28          East of England      2
## 151   2020-07-29          East of England      0
## 152   2020-07-30          East of England      0
## 153   2020-07-31          East of England      1
## 154   2020-08-01          East of England      0
## 155   2020-08-02          East of England      0
## 156   2020-08-03          East of England      0
## 157   2020-08-04          East of England      1
## 158   2020-08-05          East of England      1
## 159   2020-08-06          East of England      0
## 160   2020-08-07          East of England      1
## 161   2020-08-08          East of England      0
## 162   2020-08-09          East of England      0
## 163   2020-08-10          East of England      1
## 164   2020-08-11          East of England      2
## 165   2020-08-12          East of England      1
## 166   2020-08-13          East of England      0
## 167   2020-08-14          East of England      0
## 168   2020-08-15          East of England      1
## 169   2020-08-16          East of England      0
## 170   2020-08-17          East of England      0
## 171   2020-08-18          East of England      2
## 172   2020-08-19          East of England      1
## 173   2020-08-20          East of England      1
## 174   2020-08-21          East of England      0
## 175   2020-08-22          East of England      1
## 176   2020-08-23          East of England      1
## 177   2020-08-24          East of England      0
## 178   2020-08-25          East of England      0
## 179   2020-08-26          East of England      1
## 180   2020-08-27          East of England      1
## 181   2020-08-28          East of England      0
## 182   2020-08-29          East of England      0
## 183   2020-08-30          East of England      0
## 184   2020-08-31          East of England      0
## 185   2020-09-01          East of England      0
## 186   2020-09-02          East of England      0
## 187   2020-09-03          East of England      1
## 188   2020-09-04          East of England      1
## 189   2020-09-05          East of England      0
## 190   2020-09-06          East of England      1
## 191   2020-09-07          East of England      0
## 192   2020-09-08          East of England      0
## 193   2020-09-09          East of England      0
## 194   2020-09-10          East of England      0
## 195   2020-09-11          East of England      0
## 196   2020-09-12          East of England      0
## 197   2020-09-13          East of England      1
## 198   2020-09-14          East of England      1
## 199   2020-09-15          East of England      0
## 200   2020-03-01                   London      0
## 201   2020-03-02                   London      0
## 202   2020-03-03                   London      0
## 203   2020-03-04                   London      0
## 204   2020-03-05                   London      0
## 205   2020-03-06                   London      1
## 206   2020-03-07                   London      0
## 207   2020-03-08                   London      0
## 208   2020-03-09                   London      1
## 209   2020-03-10                   London      0
## 210   2020-03-11                   London      5
## 211   2020-03-12                   London      6
## 212   2020-03-13                   London     10
## 213   2020-03-14                   London     13
## 214   2020-03-15                   London      9
## 215   2020-03-16                   London     15
## 216   2020-03-17                   London     23
## 217   2020-03-18                   London     28
## 218   2020-03-19                   London     25
## 219   2020-03-20                   London     44
## 220   2020-03-21                   London     49
## 221   2020-03-22                   London     54
## 222   2020-03-23                   London     63
## 223   2020-03-24                   London     86
## 224   2020-03-25                   London    112
## 225   2020-03-26                   London    129
## 226   2020-03-27                   London    129
## 227   2020-03-28                   London    122
## 228   2020-03-29                   London    145
## 229   2020-03-30                   London    149
## 230   2020-03-31                   London    181
## 231   2020-04-01                   London    202
## 232   2020-04-02                   London    191
## 233   2020-04-03                   London    198
## 234   2020-04-04                   London    231
## 235   2020-04-05                   London    195
## 236   2020-04-06                   London    197
## 237   2020-04-07                   London    220
## 238   2020-04-08                   London    239
## 239   2020-04-09                   London    206
## 240   2020-04-10                   London    171
## 241   2020-04-11                   London    178
## 242   2020-04-12                   London    158
## 243   2020-04-13                   London    166
## 244   2020-04-14                   London    143
## 245   2020-04-15                   London    142
## 246   2020-04-16                   London    140
## 247   2020-04-17                   London    101
## 248   2020-04-18                   London    101
## 249   2020-04-19                   London    103
## 250   2020-04-20                   London     96
## 251   2020-04-21                   London     94
## 252   2020-04-22                   London    109
## 253   2020-04-23                   London     77
## 254   2020-04-24                   London     71
## 255   2020-04-25                   London     58
## 256   2020-04-26                   London     53
## 257   2020-04-27                   London     51
## 258   2020-04-28                   London     44
## 259   2020-04-29                   London     45
## 260   2020-04-30                   London     40
## 261   2020-05-01                   London     41
## 262   2020-05-02                   London     41
## 263   2020-05-03                   London     36
## 264   2020-05-04                   London     30
## 265   2020-05-05                   London     25
## 266   2020-05-06                   London     37
## 267   2020-05-07                   London     37
## 268   2020-05-08                   London     30
## 269   2020-05-09                   London     23
## 270   2020-05-10                   London     26
## 271   2020-05-11                   London     18
## 272   2020-05-12                   London     18
## 273   2020-05-13                   London     17
## 274   2020-05-14                   London     20
## 275   2020-05-15                   London     19
## 276   2020-05-16                   London     14
## 277   2020-05-17                   London     15
## 278   2020-05-18                   London     11
## 279   2020-05-19                   London     14
## 280   2020-05-20                   London     19
## 281   2020-05-21                   London     12
## 282   2020-05-22                   London     10
## 283   2020-05-23                   London      6
## 284   2020-05-24                   London      7
## 285   2020-05-25                   London      9
## 286   2020-05-26                   London     14
## 287   2020-05-27                   London      7
## 288   2020-05-28                   London      8
## 289   2020-05-29                   London      7
## 290   2020-05-30                   London     12
## 291   2020-05-31                   London      6
## 292   2020-06-01                   London     10
## 293   2020-06-02                   London      8
## 294   2020-06-03                   London      6
## 295   2020-06-04                   London      8
## 296   2020-06-05                   London      4
## 297   2020-06-06                   London      0
## 298   2020-06-07                   London      5
## 299   2020-06-08                   London      5
## 300   2020-06-09                   London      5
## 301   2020-06-10                   London      8
## 302   2020-06-11                   London      5
## 303   2020-06-12                   London      3
## 304   2020-06-13                   London      3
## 305   2020-06-14                   London      3
## 306   2020-06-15                   London      1
## 307   2020-06-16                   London      2
## 308   2020-06-17                   London      1
## 309   2020-06-18                   London      2
## 310   2020-06-19                   London      5
## 311   2020-06-20                   London      3
## 312   2020-06-21                   London      4
## 313   2020-06-22                   London      2
## 314   2020-06-23                   London      1
## 315   2020-06-24                   London      4
## 316   2020-06-25                   London      3
## 317   2020-06-26                   London      2
## 318   2020-06-27                   London      1
## 319   2020-06-28                   London      2
## 320   2020-06-29                   London      2
## 321   2020-06-30                   London      1
## 322   2020-07-01                   London      2
## 323   2020-07-02                   London      2
## 324   2020-07-03                   London      2
## 325   2020-07-04                   London      1
## 326   2020-07-05                   London      3
## 327   2020-07-06                   London      2
## 328   2020-07-07                   London      1
## 329   2020-07-08                   London      3
## 330   2020-07-09                   London      4
## 331   2020-07-10                   London      0
## 332   2020-07-11                   London      1
## 333   2020-07-12                   London      1
## 334   2020-07-13                   London      1
## 335   2020-07-14                   London      0
## 336   2020-07-15                   London      2
## 337   2020-07-16                   London      0
## 338   2020-07-17                   London      0
## 339   2020-07-18                   London      2
## 340   2020-07-19                   London      0
## 341   2020-07-20                   London      0
## 342   2020-07-21                   London      1
## 343   2020-07-22                   London      0
## 344   2020-07-23                   London      2
## 345   2020-07-24                   London      0
## 346   2020-07-25                   London      1
## 347   2020-07-26                   London      0
## 348   2020-07-27                   London      1
## 349   2020-07-28                   London      0
## 350   2020-07-29                   London      0
## 351   2020-07-30                   London      1
## 352   2020-07-31                   London      0
## 353   2020-08-01                   London      0
## 354   2020-08-02                   London      3
## 355   2020-08-03                   London      0
## 356   2020-08-04                   London      0
## 357   2020-08-05                   London      0
## 358   2020-08-06                   London      1
## 359   2020-08-07                   London      0
## 360   2020-08-08                   London      0
## 361   2020-08-09                   London      0
## 362   2020-08-10                   London      0
## 363   2020-08-11                   London      1
## 364   2020-08-12                   London      0
## 365   2020-08-13                   London      2
## 366   2020-08-14                   London      0
## 367   2020-08-15                   London      0
## 368   2020-08-16                   London      0
## 369   2020-08-17                   London      1
## 370   2020-08-18                   London      1
## 371   2020-08-19                   London      0
## 372   2020-08-20                   London      1
## 373   2020-08-21                   London      0
## 374   2020-08-22                   London      0
## 375   2020-08-23                   London      0
## 376   2020-08-24                   London      1
## 377   2020-08-25                   London      1
## 378   2020-08-26                   London      0
## 379   2020-08-27                   London      0
## 380   2020-08-28                   London      0
## 381   2020-08-29                   London      0
## 382   2020-08-30                   London      0
## 383   2020-08-31                   London      1
## 384   2020-09-01                   London      0
## 385   2020-09-02                   London      1
## 386   2020-09-03                   London      1
## 387   2020-09-04                   London      0
## 388   2020-09-05                   London      0
## 389   2020-09-06                   London      2
## 390   2020-09-07                   London      0
## 391   2020-09-08                   London      0
## 392   2020-09-09                   London      0
## 393   2020-09-10                   London      1
## 394   2020-09-11                   London      1
## 395   2020-09-12                   London      1
## 396   2020-09-13                   London      0
## 397   2020-09-14                   London      0
## 398   2020-09-15                   London      1
## 399   2020-03-01                 Midlands      0
## 400   2020-03-02                 Midlands      0
## 401   2020-03-03                 Midlands      1
## 402   2020-03-04                 Midlands      0
## 403   2020-03-05                 Midlands      0
## 404   2020-03-06                 Midlands      0
## 405   2020-03-07                 Midlands      0
## 406   2020-03-08                 Midlands      2
## 407   2020-03-09                 Midlands      1
## 408   2020-03-10                 Midlands      0
## 409   2020-03-11                 Midlands      2
## 410   2020-03-12                 Midlands      6
## 411   2020-03-13                 Midlands      5
## 412   2020-03-14                 Midlands      4
## 413   2020-03-15                 Midlands      5
## 414   2020-03-16                 Midlands     11
## 415   2020-03-17                 Midlands      8
## 416   2020-03-18                 Midlands     13
## 417   2020-03-19                 Midlands      8
## 418   2020-03-20                 Midlands     28
## 419   2020-03-21                 Midlands     13
## 420   2020-03-22                 Midlands     31
## 421   2020-03-23                 Midlands     33
## 422   2020-03-24                 Midlands     41
## 423   2020-03-25                 Midlands     48
## 424   2020-03-26                 Midlands     64
## 425   2020-03-27                 Midlands     72
## 426   2020-03-28                 Midlands     89
## 427   2020-03-29                 Midlands     92
## 428   2020-03-30                 Midlands     90
## 429   2020-03-31                 Midlands    123
## 430   2020-04-01                 Midlands    140
## 431   2020-04-02                 Midlands    142
## 432   2020-04-03                 Midlands    124
## 433   2020-04-04                 Midlands    151
## 434   2020-04-05                 Midlands    164
## 435   2020-04-06                 Midlands    140
## 436   2020-04-07                 Midlands    123
## 437   2020-04-08                 Midlands    186
## 438   2020-04-09                 Midlands    139
## 439   2020-04-10                 Midlands    127
## 440   2020-04-11                 Midlands    142
## 441   2020-04-12                 Midlands    139
## 442   2020-04-13                 Midlands    120
## 443   2020-04-14                 Midlands    116
## 444   2020-04-15                 Midlands    147
## 445   2020-04-16                 Midlands    102
## 446   2020-04-17                 Midlands    118
## 447   2020-04-18                 Midlands    115
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## 955   2020-08-06               North West      2
## 956   2020-08-07               North West      2
## 957   2020-08-08               North West      2
## 958   2020-08-09               North West      3
## 959   2020-08-10               North West      2
## 960   2020-08-11               North West      3
## 961   2020-08-12               North West      0
## 962   2020-08-13               North West      2
## 963   2020-08-14               North West      2
## 964   2020-08-15               North West      6
## 965   2020-08-16               North West      2
## 966   2020-08-17               North West      1
## 967   2020-08-18               North West      2
## 968   2020-08-19               North West      0
## 969   2020-08-20               North West      1
## 970   2020-08-21               North West      4
## 971   2020-08-22               North West      3
## 972   2020-08-23               North West      4
## 973   2020-08-24               North West      4
## 974   2020-08-25               North West      3
## 975   2020-08-26               North West      4
## 976   2020-08-27               North West      1
## 977   2020-08-28               North West      2
## 978   2020-08-29               North West      0
## 979   2020-08-30               North West      2
## 980   2020-08-31               North West      2
## 981   2020-09-01               North West      0
## 982   2020-09-02               North West      2
## 983   2020-09-03               North West      1
## 984   2020-09-04               North West      3
## 985   2020-09-05               North West      6
## 986   2020-09-06               North West      1
## 987   2020-09-07               North West      8
## 988   2020-09-08               North West      5
## 989   2020-09-09               North West      4
## 990   2020-09-10               North West      4
## 991   2020-09-11               North West      0
## 992   2020-09-12               North West      1
## 993   2020-09-13               North West      1
## 994   2020-09-14               North West      2
## 995   2020-09-15               North West      1
## 996   2020-03-01               South East      0
## 997   2020-03-02               South East      0
## 998   2020-03-03               South East      1
## 999   2020-03-04               South East      0
## 1000  2020-03-05               South East      1
## 1001  2020-03-06               South East      0
## 1002  2020-03-07               South East      0
## 1003  2020-03-08               South East      1
## 1004  2020-03-09               South East      1
## 1005  2020-03-10               South East      1
## 1006  2020-03-11               South East      1
## 1007  2020-03-12               South East      0
## 1008  2020-03-13               South East      1
## 1009  2020-03-14               South East      1
## 1010  2020-03-15               South East      5
## 1011  2020-03-16               South East      8
## 1012  2020-03-17               South East      7
## 1013  2020-03-18               South East     10
## 1014  2020-03-19               South East      9
## 1015  2020-03-20               South East     13
## 1016  2020-03-21               South East      7
## 1017  2020-03-22               South East     25
## 1018  2020-03-23               South East     20
## 1019  2020-03-24               South East     22
## 1020  2020-03-25               South East     29
## 1021  2020-03-26               South East     35
## 1022  2020-03-27               South East     35
## 1023  2020-03-28               South East     36
## 1024  2020-03-29               South East     55
## 1025  2020-03-30               South East     58
## 1026  2020-03-31               South East     65
## 1027  2020-04-01               South East     66
## 1028  2020-04-02               South East     55
## 1029  2020-04-03               South East     72
## 1030  2020-04-04               South East     80
## 1031  2020-04-05               South East     82
## 1032  2020-04-06               South East     88
## 1033  2020-04-07               South East    100
## 1034  2020-04-08               South East     83
## 1035  2020-04-09               South East    104
## 1036  2020-04-10               South East     88
## 1037  2020-04-11               South East     88
## 1038  2020-04-12               South East     88
## 1039  2020-04-13               South East     84
## 1040  2020-04-14               South East     65
## 1041  2020-04-15               South East     72
## 1042  2020-04-16               South East     56
## 1043  2020-04-17               South East     86
## 1044  2020-04-18               South East     57
## 1045  2020-04-19               South East     70
## 1046  2020-04-20               South East     87
## 1047  2020-04-21               South East     51
## 1048  2020-04-22               South East     54
## 1049  2020-04-23               South East     57
## 1050  2020-04-24               South East     64
## 1051  2020-04-25               South East     51
## 1052  2020-04-26               South East     51
## 1053  2020-04-27               South East     41
## 1054  2020-04-28               South East     40
## 1055  2020-04-29               South East     47
## 1056  2020-04-30               South East     29
## 1057  2020-05-01               South East     37
## 1058  2020-05-02               South East     36
## 1059  2020-05-03               South East     17
## 1060  2020-05-04               South East     35
## 1061  2020-05-05               South East     29
## 1062  2020-05-06               South East     25
## 1063  2020-05-07               South East     27
## 1064  2020-05-08               South East     26
## 1065  2020-05-09               South East     28
## 1066  2020-05-10               South East     19
## 1067  2020-05-11               South East     25
## 1068  2020-05-12               South East     27
## 1069  2020-05-13               South East     18
## 1070  2020-05-14               South East     32
## 1071  2020-05-15               South East     25
## 1072  2020-05-16               South East     22
## 1073  2020-05-17               South East     18
## 1074  2020-05-18               South East     22
## 1075  2020-05-19               South East     12
## 1076  2020-05-20               South East     22
## 1077  2020-05-21               South East     15
## 1078  2020-05-22               South East     17
## 1079  2020-05-23               South East     21
## 1080  2020-05-24               South East     17
## 1081  2020-05-25               South East     13
## 1082  2020-05-26               South East     19
## 1083  2020-05-27               South East     19
## 1084  2020-05-28               South East     12
## 1085  2020-05-29               South East     22
## 1086  2020-05-30               South East      8
## 1087  2020-05-31               South East     12
## 1088  2020-06-01               South East     11
## 1089  2020-06-02               South East     13
## 1090  2020-06-03               South East     18
## 1091  2020-06-04               South East     11
## 1092  2020-06-05               South East     11
## 1093  2020-06-06               South East     10
## 1094  2020-06-07               South East     12
## 1095  2020-06-08               South East      8
## 1096  2020-06-09               South East     10
## 1097  2020-06-10               South East     11
## 1098  2020-06-11               South East      5
## 1099  2020-06-12               South East      6
## 1100  2020-06-13               South East      7
## 1101  2020-06-14               South East      7
## 1102  2020-06-15               South East      8
## 1103  2020-06-16               South East     14
## 1104  2020-06-17               South East      9
## 1105  2020-06-18               South East      4
## 1106  2020-06-19               South East      7
## 1107  2020-06-20               South East      5
## 1108  2020-06-21               South East      3
## 1109  2020-06-22               South East      2
## 1110  2020-06-23               South East      9
## 1111  2020-06-24               South East      7
## 1112  2020-06-25               South East      5
## 1113  2020-06-26               South East      8
## 1114  2020-06-27               South East      9
## 1115  2020-06-28               South East      6
## 1116  2020-06-29               South East      5
## 1117  2020-06-30               South East      5
## 1118  2020-07-01               South East      2
## 1119  2020-07-02               South East      8
## 1120  2020-07-03               South East      3
## 1121  2020-07-04               South East      6
## 1122  2020-07-05               South East      5
## 1123  2020-07-06               South East      4
## 1124  2020-07-07               South East      6
## 1125  2020-07-08               South East      3
## 1126  2020-07-09               South East      7
## 1127  2020-07-10               South East      3
## 1128  2020-07-11               South East      4
## 1129  2020-07-12               South East      4
## 1130  2020-07-13               South East      5
## 1131  2020-07-14               South East      5
## 1132  2020-07-15               South East      6
## 1133  2020-07-16               South East      3
## 1134  2020-07-17               South East      1
## 1135  2020-07-18               South East      5
## 1136  2020-07-19               South East      2
## 1137  2020-07-20               South East      6
## 1138  2020-07-21               South East      4
## 1139  2020-07-22               South East      2
## 1140  2020-07-23               South East      3
## 1141  2020-07-24               South East      1
## 1142  2020-07-25               South East      1
## 1143  2020-07-26               South East      3
## 1144  2020-07-27               South East      1
## 1145  2020-07-28               South East      3
## 1146  2020-07-29               South East      2
## 1147  2020-07-30               South East      3
## 1148  2020-07-31               South East      1
## 1149  2020-08-01               South East      2
## 1150  2020-08-02               South East      4
## 1151  2020-08-03               South East      0
## 1152  2020-08-04               South East      0
## 1153  2020-08-05               South East      0
## 1154  2020-08-06               South East      2
## 1155  2020-08-07               South East      0
## 1156  2020-08-08               South East      2
## 1157  2020-08-09               South East      0
## 1158  2020-08-10               South East      2
## 1159  2020-08-11               South East      1
## 1160  2020-08-12               South East      1
## 1161  2020-08-13               South East      0
## 1162  2020-08-14               South East      0
## 1163  2020-08-15               South East      2
## 1164  2020-08-16               South East      1
## 1165  2020-08-17               South East      0
## 1166  2020-08-18               South East      2
## 1167  2020-08-19               South East      1
## 1168  2020-08-20               South East      0
## 1169  2020-08-21               South East      0
## 1170  2020-08-22               South East      0
## 1171  2020-08-23               South East      1
## 1172  2020-08-24               South East      0
## 1173  2020-08-25               South East      1
## 1174  2020-08-26               South East      0
## 1175  2020-08-27               South East      1
## 1176  2020-08-28               South East      1
## 1177  2020-08-29               South East      1
## 1178  2020-08-30               South East      0
## 1179  2020-08-31               South East      2
## 1180  2020-09-01               South East      1
## 1181  2020-09-02               South East      1
## 1182  2020-09-03               South East      0
## 1183  2020-09-04               South East      1
## 1184  2020-09-05               South East      0
## 1185  2020-09-06               South East      1
## 1186  2020-09-07               South East      0
## 1187  2020-09-08               South East      0
## 1188  2020-09-09               South East      0
## 1189  2020-09-10               South East      1
## 1190  2020-09-11               South East      1
## 1191  2020-09-12               South East      0
## 1192  2020-09-13               South East      2
## 1193  2020-09-14               South East      0
## 1194  2020-09-15               South East      0
## 1195  2020-03-01               South West      0
## 1196  2020-03-02               South West      0
## 1197  2020-03-03               South West      0
## 1198  2020-03-04               South West      0
## 1199  2020-03-05               South West      0
## 1200  2020-03-06               South West      0
## 1201  2020-03-07               South West      0
## 1202  2020-03-08               South West      0
## 1203  2020-03-09               South West      0
## 1204  2020-03-10               South West      0
## 1205  2020-03-11               South West      1
## 1206  2020-03-12               South West      0
## 1207  2020-03-13               South West      0
## 1208  2020-03-14               South West      1
## 1209  2020-03-15               South West      0
## 1210  2020-03-16               South West      0
## 1211  2020-03-17               South West      2
## 1212  2020-03-18               South West      2
## 1213  2020-03-19               South West      4
## 1214  2020-03-20               South West      3
## 1215  2020-03-21               South West      6
## 1216  2020-03-22               South West      7
## 1217  2020-03-23               South West      8
## 1218  2020-03-24               South West      7
## 1219  2020-03-25               South West      9
## 1220  2020-03-26               South West     11
## 1221  2020-03-27               South West     13
## 1222  2020-03-28               South West     21
## 1223  2020-03-29               South West     18
## 1224  2020-03-30               South West     23
## 1225  2020-03-31               South West     23
## 1226  2020-04-01               South West     21
## 1227  2020-04-02               South West     23
## 1228  2020-04-03               South West     30
## 1229  2020-04-04               South West     42
## 1230  2020-04-05               South West     32
## 1231  2020-04-06               South West     34
## 1232  2020-04-07               South West     39
## 1233  2020-04-08               South West     47
## 1234  2020-04-09               South West     24
## 1235  2020-04-10               South West     46
## 1236  2020-04-11               South West     43
## 1237  2020-04-12               South West     23
## 1238  2020-04-13               South West     27
## 1239  2020-04-14               South West     24
## 1240  2020-04-15               South West     32
## 1241  2020-04-16               South West     29
## 1242  2020-04-17               South West     33
## 1243  2020-04-18               South West     25
## 1244  2020-04-19               South West     31
## 1245  2020-04-20               South West     26
## 1246  2020-04-21               South West     26
## 1247  2020-04-22               South West     23
## 1248  2020-04-23               South West     17
## 1249  2020-04-24               South West     19
## 1250  2020-04-25               South West     15
## 1251  2020-04-26               South West     27
## 1252  2020-04-27               South West     13
## 1253  2020-04-28               South West     17
## 1254  2020-04-29               South West     15
## 1255  2020-04-30               South West     26
## 1256  2020-05-01               South West      6
## 1257  2020-05-02               South West      7
## 1258  2020-05-03               South West     10
## 1259  2020-05-04               South West     17
## 1260  2020-05-05               South West     14
## 1261  2020-05-06               South West     19
## 1262  2020-05-07               South West     16
## 1263  2020-05-08               South West      6
## 1264  2020-05-09               South West     11
## 1265  2020-05-10               South West      5
## 1266  2020-05-11               South West      8
## 1267  2020-05-12               South West      7
## 1268  2020-05-13               South West      7
## 1269  2020-05-14               South West      6
## 1270  2020-05-15               South West      4
## 1271  2020-05-16               South West      4
## 1272  2020-05-17               South West      6
## 1273  2020-05-18               South West      4
## 1274  2020-05-19               South West      6
## 1275  2020-05-20               South West      1
## 1276  2020-05-21               South West      9
## 1277  2020-05-22               South West      7
## 1278  2020-05-23               South West      6
## 1279  2020-05-24               South West      3
## 1280  2020-05-25               South West      8
## 1281  2020-05-26               South West     11
## 1282  2020-05-27               South West      5
## 1283  2020-05-28               South West     10
## 1284  2020-05-29               South West      7
## 1285  2020-05-30               South West      3
## 1286  2020-05-31               South West      2
## 1287  2020-06-01               South West      7
## 1288  2020-06-02               South West      2
## 1289  2020-06-03               South West      7
## 1290  2020-06-04               South West      2
## 1291  2020-06-05               South West      2
## 1292  2020-06-06               South West      1
## 1293  2020-06-07               South West      3
## 1294  2020-06-08               South West      3
## 1295  2020-06-09               South West      0
## 1296  2020-06-10               South West      1
## 1297  2020-06-11               South West      2
## 1298  2020-06-12               South West      2
## 1299  2020-06-13               South West      2
## 1300  2020-06-14               South West      0
## 1301  2020-06-15               South West      2
## 1302  2020-06-16               South West      2
## 1303  2020-06-17               South West      0
## 1304  2020-06-18               South West      0
## 1305  2020-06-19               South West      0
## 1306  2020-06-20               South West      2
## 1307  2020-06-21               South West      0
## 1308  2020-06-22               South West      1
## 1309  2020-06-23               South West      1
## 1310  2020-06-24               South West      1
## 1311  2020-06-25               South West      0
## 1312  2020-06-26               South West      3
## 1313  2020-06-27               South West      0
## 1314  2020-06-28               South West      0
## 1315  2020-06-29               South West      1
## 1316  2020-06-30               South West      0
## 1317  2020-07-01               South West      0
## 1318  2020-07-02               South West      0
## 1319  2020-07-03               South West      0
## 1320  2020-07-04               South West      0
## 1321  2020-07-05               South West      1
## 1322  2020-07-06               South West      0
## 1323  2020-07-07               South West      0
## 1324  2020-07-08               South West      2
## 1325  2020-07-09               South West      0
## 1326  2020-07-10               South West      1
## 1327  2020-07-11               South West      0
## 1328  2020-07-12               South West      0
## 1329  2020-07-13               South West      1
## 1330  2020-07-14               South West      0
## 1331  2020-07-15               South West      0
## 1332  2020-07-16               South West      0
## 1333  2020-07-17               South West      1
## 1334  2020-07-18               South West      0
## 1335  2020-07-19               South West      0
## 1336  2020-07-20               South West      0
## 1337  2020-07-21               South West      0
## 1338  2020-07-22               South West      0
## 1339  2020-07-23               South West      0
## 1340  2020-07-24               South West      0
## 1341  2020-07-25               South West      0
## 1342  2020-07-26               South West      0
## 1343  2020-07-27               South West      0
## 1344  2020-07-28               South West      0
## 1345  2020-07-29               South West      0
## 1346  2020-07-30               South West      1
## 1347  2020-07-31               South West      0
## 1348  2020-08-01               South West      0
## 1349  2020-08-02               South West      0
## 1350  2020-08-03               South West      0
## 1351  2020-08-04               South West      0
## 1352  2020-08-05               South West      0
## 1353  2020-08-06               South West      0
## 1354  2020-08-07               South West      0
## 1355  2020-08-08               South West      0
## 1356  2020-08-09               South West      0
## 1357  2020-08-10               South West      0
## 1358  2020-08-11               South West      0
## 1359  2020-08-12               South West      0
## 1360  2020-08-13               South West      0
## 1361  2020-08-14               South West      1
## 1362  2020-08-15               South West      0
## 1363  2020-08-16               South West      0
## 1364  2020-08-17               South West      2
## 1365  2020-08-18               South West      0
## 1366  2020-08-19               South West      0
## 1367  2020-08-20               South West      0
## 1368  2020-08-21               South West      0
## 1369  2020-08-22               South West      0
## 1370  2020-08-23               South West      0
## 1371  2020-08-24               South West      0
## 1372  2020-08-25               South West      1
## 1373  2020-08-26               South West      0
## 1374  2020-08-27               South West      1
## 1375  2020-08-28               South West      0
## 1376  2020-08-29               South West      0
## 1377  2020-08-30               South West      0
## 1378  2020-08-31               South West      0
## 1379  2020-09-01               South West      0
## 1380  2020-09-02               South West      0
## 1381  2020-09-03               South West      0
## 1382  2020-09-04               South West      0
## 1383  2020-09-05               South West      0
## 1384  2020-09-06               South West      0
## 1385  2020-09-07               South West      0
## 1386  2020-09-08               South West      1
## 1387  2020-09-09               South West      0
## 1388  2020-09-10               South West      0
## 1389  2020-09-11               South West      0
## 1390  2020-09-12               South West      0
## 1391  2020-09-13               South West      0
## 1392  2020-09-14               South West      0
## 1393  2020-09-15               South West      0

1.5 Completion date

We extract the completion date from the NHS Pathways file timestamp:


database_date <- attr(x, "timestamp")
database_date
## [1] "2020-09-16"

The completion date of the NHS Pathways data is Wednesday 16 Sep 2020.

1.6 Auxiliary functions

These are functions which will be used further in the analyses.

Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:


## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here

Rsq <- function(x) {
  1 - (x$deviance / x$null.deviance)
}

Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:


## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals

get_r <- function(model) {
  ##  extract coefficients and conf int
  out <- data.frame(r = coef(model))  %>%
    rownames_to_column("var") %>% 
    cbind(confint(model)) %>%
    filter(!grepl("day_of_week", var)) %>% 
    filter(grepl("day", var)) %>%
    rename(lower_95 = "2.5 %",
           upper_95 = "97.5 %") %>%
    mutate(var = sub("day:", "", var))
  
  ## reconstruct values: intercept + region-coefficient
  for (i in 2:nrow(out)) {
    out[i, -1] <- out[1, -1] + out[i, -1]
  }
  
  ## find the name of the intercept, restore regions names
  out <- out %>%
    mutate(nhs_region = model$xlevels$nhs_region) %>%
    select(nhs_region, everything(), -var)
  
  ## find halving times
  halving <- log(0.5) / out[,-1] %>%
    rename(halving_t = r,
           halving_t_lower_95 = lower_95,
           halving_t_upper_95 = upper_95)
  
  ## set halving times with exclusion intervals to NA
  no_halving <- out$lower_95 < 0 & out$upper_95 > 0
  halving[no_halving, ] <- NA_real_
  
  ## return all data
  cbind(out, halving)
  
}

Functions used in the correlation analysis between NHS Pathways reports and deaths:

## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.

getcor <- function(x, ndx) {
  return(cor(x$deaths[ndx],
             x$note_lag[ndx],
             use = "complete.obs",
             method = "pearson"))
}

## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)

getboot <- function(x) {
  result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000), 
                           type = "bca")
  return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
                    r = result$t0,
                    r_low = result$bca[4],
                    r_hi = result$bca[5]))
}

Function to classify the day of the week into weekend, Monday, and the rest:


## Fn to add day of week
day_of_week <- function(df) {
  df %>% 
    dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>% 
    dplyr::mutate(day_of_week = dplyr::case_when(
      day_of_week %in% c("Sat", "Sun") ~ "weekend",
      day_of_week %in% c("Mon") ~ "monday",
      !(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
    ) %>% 
      factor(levels = c("rest_of_week", "monday", "weekend")))
}

Custom color palettes, color scales, and vectors of colors:


pal <- c("#006212",
         "#ae3cab",
         "#00db90",
         "#960c00",
         "#55aaff",
         "#ff7e78",
         "#00388d")

age.pal <- viridis::viridis(3,begin = 0.1, end = 0.7)

3 Comparison with deaths time series

3.1 Outline

We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.

Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.

3.2 Lagged correlation

We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.

First we join the NHS Pathways and death data, and aggregate over all England:

## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max

dth_trunc <- dth %>%
  rename(date = date_report) %>%
  filter(date <= trunc_date) 

## join with notification data
all_data <- x %>% 
  filter(!is.na(nhs_region)) %>%
  group_by(date, nhs_region) %>%
  summarise(count = sum(count, na.rm = T)) %>%
  ungroup %>%
  inner_join(dth_trunc,
             by = c("date","nhs_region"))

all_tot <- all_data %>%
  group_by(date) %>%
  summarise(count = sum(count, na.rm = TRUE),
            deaths = sum(deaths, na.rm = TRUE)) 

We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:


## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
  
  ## lag reports
  summary <- all_tot %>% 
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI
    getboot(.) %>%
    mutate(lag = i)

  lag_cor <- bind_rows(lag_cor, summary)
}

cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
  theme_bw() +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_point() +
  geom_line() +
  labs(x = "Lag between NHS pathways and death data (days)",
       y = "Pearson's correlation") +
  large_txt
cor_vs_lag


l_opt <- which.max(lag_cor$r)

This analysis suggests that the best lag is 23 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 23 days.


all_tot <- all_tot %>%
  rename(date_death = date) %>%
  mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
         note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
         date_note = lag(date_death,16))

lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")

summary(lag_mod)
## 
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -19.929   -7.715   -2.988    4.355   13.380  
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 4.007e+00  8.337e-02   48.06   <2e-16 ***
## note_lag    1.935e-05  8.654e-07   22.36   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for quasipoisson family taken to be 49.72135)
## 
##     Null deviance: 28329.7  on 137  degrees of freedom
## Residual deviance:  7261.8  on 136  degrees of freedom
##   (23 observations deleted due to missingness)
## AIC: NA
## 
## Number of Fisher Scoring iterations: 5

exp(coefficients(lag_mod))
## (Intercept)    note_lag 
##   54.983839    1.000019
exp(confint(lag_mod))
##                 2.5 %    97.5 %
## (Intercept) 46.517792 64.510029
## note_lag     1.000018  1.000021

Rsq(lag_mod)
## [1] 0.743667

mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])

all_tot_pred <- 
  all_tot %>%
  filter(!is.na(note_lag)) %>%
  mutate(pred = mod_fit$fit,
         pred.se = mod_fit$se.fit,
         low = exp(pred - 1.96*pred.se),
         hi = exp(pred + 1.96*pred.se))


glm_fit <- all_tot_pred %>% 
    filter(!is.na(note_lag)) %>%
  ggplot(aes(x = note_lag, y = deaths)) +
  geom_point() + 
  geom_line(aes(y = exp(pred))) + 
  geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
  theme_bw() +
  labs(y = "Daily number of\ndeaths reported",
       x = "Daily number of NHS Pathways reports") +
  large_txt

glm_fit

4 Supplementary figures

4.1 Serial interval distribution

This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.

SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale, w = 0.5)

SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
                                        meanlog = log(4.7),
                                        sdlog = log(2.9), w = 0.5)

SI_dist1 <- data.frame(x = SI_distribution$r(1e5)) 
SI_dist1 <- count(SI_dist1, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 30, 5)) +
    theme_bw()

SI_dist2 <- data.frame(x = SI_distribution2$r(1e5)) 
SI_dist2 <- count(SI_dist2, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
    theme_bw()


ggpubr::ggarrange(SI_dist1,
                  SI_dist2,
                  nrow = 1,
                  labels = "AUTO") 

4.2 Sensitivity analysis - 7 or 21 days moving window

We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.

First with the 7 days window:

## set moving time window (1/2/3 weeks)
w <- 7

# create empty df
r_all_sliding_7days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
plot_R <- r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_7days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_7days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_7 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

Then with the 21 days window:

## set moving time window (1/2/3 weeks)
w <- 21

# create empty df
r_all_sliding_21days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
# plot
plot_R <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_21days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_21days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_21 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

And we combine both outputs into a single plot:


ggpubr::ggarrange(r_R_7,
                  r_R_21,
                  nrow = 2,
                  labels = "AUTO",
                  common.legend = TRUE,
                  legend = "bottom") 

4.3 Correlation between NHS Pathways reports and deaths by NHS region


lag_cor_reg <- data.frame()

for (i in 0:30) {

  summary <-
    all_data %>%
    group_by(nhs_region) %>%
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI for each region
    group_modify(~getboot(.x)) %>%
    mutate(lag = i)
  
  lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}

cor_vs_lag_reg <- 
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
  geom_point() +
  geom_line() +
  facet_wrap(~nhs_region) +
  scale_color_manual(values = pal) +
  scale_fill_manual(values = pal, guide = F) +  
  theme_bw() +
  labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
  theme(legend.position = "bottom") +
  guides(color = guide_legend(override.aes = list(fill = NA)))

cor_vs_lag_reg

5 Export data

We save the tables created during our analysis:


if (!dir.exists("excel_tables")) {
  dir.create("excel_tables")
}


## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")

for (e in tables_to_export) {
  rio::export(get(e),
              file.path("excel_tables",
                        paste0(e, ".xlsx")))
}

## also export result from regression on lagged data 
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))

6 System information

6.1 Outline

The following information documents the system on which the document was compiled.

6.2 System

This provides information on the operating system.

Sys.info()
##                                                                                            sysname 
##                                                                                           "Darwin" 
##                                                                                            release 
##                                                                                           "19.6.0" 
##                                                                                            version 
## "Darwin Kernel Version 19.6.0: Thu Jun 18 20:49:00 PDT 2020; root:xnu-6153.141.1~1/RELEASE_X86_64" 
##                                                                                           nodename 
##                                                                          "Mac-1600337236613.local" 
##                                                                                            machine 
##                                                                                           "x86_64" 
##                                                                                              login 
##                                                                                             "root" 
##                                                                                               user 
##                                                                                           "runner" 
##                                                                                     effective_user 
##                                                                                           "runner"

6.3 R environment

This provides information on the version of R used:

R.version
##                _                           
## platform       x86_64-apple-darwin17.0     
## arch           x86_64                      
## os             darwin17.0                  
## system         x86_64, darwin17.0          
## status                                     
## major          4                           
## minor          0.2                         
## year           2020                        
## month          06                          
## day            22                          
## svn rev        78730                       
## language       R                           
## version.string R version 4.0.2 (2020-06-22)
## nickname       Taking Off Again

6.4 R packages

This provides information on the packages used:

sessionInfo()
## R version 4.0.2 (2020-06-22)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Catalina 10.15.6
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggnewscale_0.4.3     ggpubr_0.4.0         lubridate_1.7.9     
##  [4] chngpt_2020.8-29     cyphr_1.1.0          DT_0.15             
##  [7] kableExtra_1.2.1     janitor_2.0.1        remotes_2.2.0       
## [10] projections_0.5.1    earlyR_0.0.1         epitrix_0.2.2       
## [13] distcrete_1.0.3      incidence_1.7.2      rio_0.5.16          
## [16] reshape2_1.4.4       rvest_0.3.6          xml2_1.3.2          
## [19] linelist_0.0.40.9000 forcats_0.5.0        stringr_1.4.0       
## [22] dplyr_1.0.2          purrr_0.3.4          readr_1.3.1         
## [25] tidyr_1.1.2          tibble_3.0.3         ggplot2_3.3.2       
## [28] tidyverse_1.3.0      here_0.1             reportfactory_0.0.5 
## 
## loaded via a namespace (and not attached):
##  [1] minqa_1.2.4       colorspace_1.4-1  selectr_0.4-2     ggsignif_0.6.0   
##  [5] ellipsis_0.3.1    rprojroot_1.3-2   snakecase_0.11.0  fs_1.5.0         
##  [9] rstudioapi_0.11   farver_2.0.3      fansi_0.4.1       splines_4.0.2    
## [13] knitr_1.29        jsonlite_1.7.1    nloptr_1.2.2.2    broom_0.7.0      
## [17] dbplyr_1.4.4      compiler_4.0.2    httr_1.4.2        backports_1.1.10 
## [21] assertthat_0.2.1  Matrix_1.2-18     cli_2.0.2         htmltools_0.5.0  
## [25] tools_4.0.2       gtable_0.3.0      glue_1.4.2        Rcpp_1.0.5       
## [29] carData_3.0-4     cellranger_1.1.0  vctrs_0.3.4       nlme_3.1-148     
## [33] matchmaker_0.1.1  crosstalk_1.1.0.1 xfun_0.17         openxlsx_4.2.2   
## [37] lme4_1.1-23       lifecycle_0.2.0   statmod_1.4.34    rstatix_0.6.0    
## [41] MASS_7.3-51.6     scales_1.1.1      hms_0.5.3         sodium_1.1       
## [45] yaml_2.2.1        curl_4.3          gridExtra_2.3     stringi_1.5.3    
## [49] kyotil_2020.8-22  boot_1.3-25       zip_2.1.1         rlang_0.4.7      
## [53] pkgconfig_2.0.3   evaluate_0.14     lattice_0.20-41   htmlwidgets_1.5.1
## [57] labeling_0.3      cowplot_1.1.0     tidyselect_1.1.0  plyr_1.8.6       
## [61] magrittr_1.5      R6_2.4.1          generics_0.0.2    DBI_1.1.0        
## [65] pillar_1.4.6      haven_2.3.1       foreign_0.8-80    withr_2.2.0      
## [69] mgcv_1.8-31       survival_3.1-12   abind_1.4-5       modelr_0.1.8     
## [73] crayon_1.3.4      car_3.0-9         utf8_1.1.4        rmarkdown_2.3    
## [77] viridis_0.5.1     grid_4.0.2        readxl_1.3.1      data.table_1.13.0
## [81] blob_1.2.1        reprex_0.3.0      digest_0.6.25     webshot_0.5.2    
## [85] munsell_0.5.0     viridisLite_0.3.0